Fluorescence resonance energy transfer (FRET) imaging is a microscope technique that uses a dye pair. It detects bonding of proteins, and in turn, is used to deduce many activities such as chromosome dynamics through the cell cycle. When one dye (the donor), gives up an energy state, instead of converting the energy into a photon, it transfers the energy to a nearby acceptor dye molecule. The acceptor molecule then emits a photon which is detected by the camera. When this happens, the donor and acceptor must be within nanometers of one another and are probably bound to the same protein. This way, protein bondings are monitored. The long-term objective of this research is to provide a profitable commercial software product that makes FRET imaging straightforward, inexpensive and accurate. FRET requires an image processing algorithm to see the regions in a biological sample where the FRET activity, and thus the chemical bonds, are happening. The algorithms that are used widely today have mathematical approximations that are often not accurate and therefore cause reliability questions. The main physical cause that underlies these mathematical approximations is that the fluorescent dye pairs have severe cross-talk and bleed-through among their excitation and emission spectra. Paradoxically, this cross-talk and bleed-through are necessary for FRET to occur, so it is impossible to avoid them. Mathematically, there are more unknowns than simultaneous equations, and therefore there is a fundamentally unsolvable mathematical problem. The software proposed herein overcomes these mathematical problems. It is based upon Maximum Likelihood Estimation, which eliminates the need for simultaneous equations, and instead provides a solution based upon the maximum-likelihood criterion. The specific aims of this research are: (1) Develop a prototype software algorithm. (2) Show feasibility of providing accurate images. This aim will be accomplished by processing biological data sets and test data from a specimen of known FRET indices.